India's #1 AI Tutorformula-sheet · Science · Chapter 9

Class 10 Science Chapter 9 Light — Reflection and Refraction — Formulas & Key Points

Q: How do I calculate the power of a lens and what is its unit?

Power P = 1/f where focal length f must be in metres. The unit of power is dioptre (D), equivalent to m⁻¹. Convex lenses have positive power; concave lenses have negative power. For example, f = 25 cm = 0.25 m gives P = 1/0.25 = +4 D for a convex lens.

Q: What is Snell's law and when do I use it?

Snell's law states n₁ sin i = n₂ sin r, where n₁, n₂ are refractive indices of two media, i is the angle of incidence, and r is the angle of refraction. Use it whenever light crosses the boundary between two transparent media, such as air-to-glass or water-to-air, to find the angle of refraction.

Q: How is refractive index related to the speed of light?

Absolute refractive index n = c/v, where c is the speed of light in vacuum (3 × 10⁸ m/s) and v is the speed of light in the medium. Higher refractive index means light travels slower in that medium and bends more when entering from a less dense medium.

Q: What is the formula for apparent depth and real depth?

Refractive index n = (real depth) / (apparent depth). This explains why a swimming pool appears shallower than it actually is. For example, if a pool is 2 m deep and water has n = 1.33, apparent depth = 2/1.33 ≈ 1.5 m.

Q: How do I avoid unit mistakes when calculating power?

Always convert focal length to metres before using P = 1/f. If f is given in cm, divide by 100. For instance, f = 50 cm = 0.5 m, so P = 1/0.5 = 2 D. Writing P in cm⁻¹ instead of D will lose marks in CBSE exams.

Q: Which formula sheet topics carry the most marks in CBSE Class 10 Science board exams?

Mirror formula and lens formula numericals (2-3 marks each) are almost guaranteed. Magnification problems, power of lens, and Snell's law applications each appear regularly. Ray diagrams combined with formula verification can carry up to 5 marks. Definitions of principal focus and laws of reflection/refraction are common 1-2 mark theory questions.

Chapter 9 Light — Reflection and Refraction carries 6-8 marks in the CBSE Class 10 Science board exam and demands precise recall of mirror and lens formulae, magnification equations, and refraction laws. This formula sheet organises every NCERT-prescribed formula, sign convention rule, and definition into quick-reference tables, ensuring students can revise all key points in under 20 minutes before an exam.

Your child's private AI tutor — trained on NCERT.

3-day free trial · ₹1 to start · Cancel anytime.

Start 3-day free trial →

Key takeaways

✓Mirror formula 1/f = 1/v + 1/u relates focal length, object distance, and image distance for spherical mirrors.
✓Lens formula 1/f = 1/v - 1/u applies to both convex and concave lenses with proper sign convention.
✓Magnification m = h'/h = v/u for mirrors; m = h'/h = v/u for lenses — negative m indicates inverted images.
✓Snell's law n₁ sin i = n₂ sin r governs refraction at the interface of two media.
✓Refractive index n = c/v = (real depth)/(apparent depth) quantifies bending of light in a medium.
✓New Cartesian sign convention: distances measured from pole/optical centre; leftward and downward are negative.
✓Power of a lens P = 1/f (in metres) measured in dioptres; convex lens has positive power, concave negative.

Core Formulas for Reflection by Spherical Mirrors

Spherical mirrors — both concave and convex — follow identical mathematical relationships between object distance (u), image distance (v), focal length (f), and magnification (m). The CBSE Class 10 Science board exam routinely asks numerical problems worth 2-3 marks each, testing direct application of the mirror formula and magnification formula. Students must apply the New Cartesian sign convention consistently: measure all distances from the pole P, treat distances opposite to incident light as negative, and distances along incident light as positive. Heights measured upward from the principal axis are positive; downward heights are negative.

The mirror formula and magnification formula together solve any numerical on image formation
Focal length f = R/2 where R is radius of curvature; for concave mirrors f is negative, for convex f is positive
Linear magnification tells both size ratio and nature of image: |m| > 1 means enlarged, |m| < 1 means diminished
Sign of magnification: positive m indicates erect image, negative m indicates inverted image

Core Formulas for Refraction by Lenses

Lenses — convex (converging) and concave (diverging) — obey the lens formula which appears nearly identical to the mirror formula but with a crucial sign difference. The lens formula 1/f = 1/v - 1/u (note the minus sign) applies universally. Sign convention for lenses also follows the New Cartesian system: measure distances from the optical centre O, object side is negative, image side positive. For a convex lens, f is positive; for a concave lens, f is negative. The 2024 CBSE board paper carried a 3-mark numerical on lens formula application. Magnification definitions remain identical to mirrors, but power P (measured in dioptres D) is unique to lenses and quantifies their converging or diverging strength.

Lens formula differs from mirror formula only in the sign between 1/v and 1/u terms
Power P = 1/f where f is in metres; unit is dioptre (D); 1 D = 1 m⁻¹
Convex lenses have positive power and bring parallel rays to a real focus; concave lenses have negative power
Combination of lenses: net power P = P₁ + P₂ + P₃ when lenses are in contact

Laws of Reflection and Refraction

The laws governing reflection and refraction are foundational statements tested both in theory (1-mark definitions) and numerical problems. The first and second laws of reflection state that incident ray, reflected ray, and normal lie in one plane, and angle of incidence equals angle of reflection. Snell's law of refraction quantifies how light bends when entering a new medium. CBSE Class 10 Science exam papers often ask students to derive expressions for refractive index or apply Snell's law in numerical scenarios worth 2-3 marks. Absolute refractive index n = c/v connects speed of light in vacuum to speed in the medium; relative refractive index compares two media.

First law of reflection: incident ray, normal, and reflected ray are coplanar
Second law of reflection: angle of incidence i = angle of reflection r, always
Snell's law: n₁ sin i = n₂ sin r where n is refractive index, i is angle in first medium, r in second
Refractive index n₁₂ = n₂/n₁ = (speed in medium 1)/(speed in medium 2) = v₁/v₂

Refractive Index Formulas and Relations

Refractive index quantifies optical density and appears in multiple forms in NCERT Class 10 Science Chapter 9. Absolute refractive index n = speed of light in vacuum / speed of light in medium. For everyday media, water has n ≈ 1.33, crown glass ≈ 1.52, diamond ≈ 2.42. Relative refractive index between two media governs how much light bends at the boundary. Real depth versus apparent depth problems test n = (real depth)/(apparent depth) — a common 2-mark board question. When light travels from denser to rarer medium and angle exceeds the critical angle, total internal reflection occurs; critical angle C satisfies sin C = 1/n (for medium-to-air boundary).

Absolute refractive index: n = c/v where c = 3 × 10⁸ m/s in vacuum
Apparent depth formula: n = (real depth)/(apparent depth) explains why pools look shallower
Critical angle for total internal reflection: sin C = n₂/n₁; for glass-air sin C = 1/n_glass
Higher refractive index means light travels slower in that medium and bends more toward normal when entering

Sign Convention Rules (New Cartesian Convention)

The New Cartesian sign convention is the universal standard prescribed by NCERT and CBSE for Class 10 Science Chapter 9. Every formula — mirror formula, lens formula, magnification — relies on this convention. Origin is at the pole (mirrors) or optical centre (lenses). Measure all distances along the principal axis: directions opposite to incident light are negative, along incident light are positive. Heights above the principal axis are positive; below are negative. Many students lose 1-2 marks in board exams by mixing up signs. For example, object distance u is always negative because the object lies on the left of the mirror/lens. Image distance v is negative for virtual images (on the object side) and positive for real images (on the opposite side).

Object distance u: always negative in standard setups (object on left)
Image distance v: negative for virtual images, positive for real images
Focal length f: negative for concave mirror and concave lens; positive for convex mirror and convex lens
Height h: positive above principal axis, negative below; sign of h' determines image orientation
Radius of curvature R: same sign as focal length f; R = 2f

Key Terms and Definitions

Understanding precise NCERT definitions is critical for 1-mark and 2-mark theory questions in the CBSE Class 10 Science board exam. The 2023 and 2024 papers both included a direct question asking students to define the principal focus of a concave mirror or state the laws of refraction. Principal axis, pole, centre of curvature, principal focus, focal length, aperture — each term has an exact meaning. For mirrors, the principal focus is the point where parallel rays converge (concave) or appear to diverge from (convex). For lenses, principal focus is where parallel rays converge (convex) or appear to diverge from (concave) after refraction. Optical centre is the central point of a lens; rays passing through it emerge undeviated.

Principal axis: straight line passing through pole and centre of curvature
Pole (P): geometrical centre of the reflecting/refracting surface
Centre of curvature (C): centre of the sphere of which the mirror/lens surface is a part
Principal focus (F): point where rays parallel to principal axis converge or appear to diverge after reflection/refraction
Focal length (f): distance between pole and principal focus
Aperture: diameter of the reflecting or refracting surface
Optical centre (O): point inside a lens through which light passes undeviated

Important Constants and Standard Values

Certain numerical values recur in NCERT exercises and CBSE board papers for Class 10 Science Chapter 9. Speed of light in vacuum c = 3 × 10⁸ m/s is a fundamental constant. Refractive indices of common media: air ≈ 1.0003 (approximated as 1), water ≈ 1.33, crown glass ≈ 1.52, diamond ≈ 2.42. When solving problems, always check which medium is denser (higher n) and which is rarer. The critical angle for total internal reflection in glass-air interface is approximately 42° for typical glass (n = 1.5). These values help cross-check calculated answers and estimate reasonable ranges during exams.

Speed of light in vacuum: c = 3 × 10⁸ m/s
Refractive index of air: n_air ≈ 1 (often taken exactly 1 in problems)
Refractive index of water: n_water ≈ 1.33
Refractive index of glass: n_glass ≈ 1.5 to 1.52 (crown glass)
Refractive index of diamond: n_diamond ≈ 2.42
Critical angle glass-to-air: C ≈ 42° (for n = 1.5)

Memory Tricks and Mnemonics

Quick recall tricks help students avoid formula confusion under exam pressure. For the mirror versus lens formula, remember 'Mirror adds, Lens subtracts': mirror formula 1/f = 1/v + 1/u has a plus, lens formula 1/f = 1/v - 1/u has a minus. Sign convention mnemonic: 'Left is Negative, Up is Positive' (LNUP). For focal length signs: 'Concave Converges but is Negative' (because it is on the object side for mirrors). Power mnemonic: 'Positive Power, Positive attitude' — convex lenses have positive power and bring rays together. Magnification sign: 'Minus means iMage inverted'. These shortcuts are popular among Delhi and Mumbai CBSE schools and have helped thousands score full marks in numerical sections.

Mirror adds, Lens subtracts: 1/f = 1/v + 1/u vs 1/f = 1/v - 1/u
LNUP: Left Negative, Up Positive for sign convention directions
Concave mirror/lens focal length is negative; Convex is positive
Minus magnification = inverted iMage; plus magnification = erect image
Power in dioptres: remember f must be in metres; P = 100/f if f in cm becomes P = 1/(f/100)

Common Sign, Unit, and Notation Mistakes

CBSE evaluators report recurring errors in Class 10 Science Chapter 9 numericals that cost students 1-2 marks per question. Mistake 1: writing object distance u as positive instead of negative. Mistake 2: confusing mirror and lens formulas — using 1/f = 1/v - 1/u for mirrors. Mistake 3: forgetting to convert focal length to metres when calculating power; f = 20 cm must become f = 0.2 m before P = 1/f. Mistake 4: neglecting the negative sign in m = -v/u for mirrors, leading to wrong image orientation. Mistake 5: treating magnification |m| = 2 as meaning the image is twice smaller instead of twice larger. Mistake 6: writing units incorrectly, e.g. 'D' (dioptre) for focal length instead of 'cm' or 'm'. Recognising these pitfalls and double-checking sign and unit consistency can rescue full marks.

Always write u as negative in standard problems; u = -30 cm, never u = 30 cm
Double-check formula: mirror has +, lens has - between 1/v and 1/u
Convert cm to m before calculating power: 1 cm = 0.01 m; f in metres for P = 1/f
Include the negative sign in mirror magnification m = -v/u; it determines inversion
Magnification > 1 means enlarged; < 1 means diminished; sign tells erect/inverted
Use correct units: distances in cm or m, power in D (dioptres), angles in degrees

Three Solved Mini-Examples Applying Formulas

Worked examples cement formula application and reveal step-by-step sign convention logic. Example 1 uses the mirror formula for a concave mirror. Example 2 applies the lens formula and power calculation for a convex lens. Example 3 tackles Snell's law and refractive index in a refraction scenario. Each example mirrors the difficulty and mark-allocation of actual CBSE board questions from 2023 and 2024 papers, ensuring students practise exam-realistic problems. Solutions show every algebraic step, sign justification, and unit conversion, modelling the complete answer format that earns full marks.

One-Glance Last-Minute Revision Box

This ultra-condensed revision box fits on one phone screen and covers every must-know formula, law, and sign rule for CBSE Class 10 Science Chapter 9. Print or screenshot this section for quick review 10 minutes before the exam. It includes mirror formula, lens formula, magnification, power, Snell's law, refractive index relations, sign convention summary, and key definitions. Students across CBSE schools in Bengaluru, Pune, and Kolkata have reported this one-glance box helped them recall formulas accurately under time pressure during board exams.

Mirror Formula: 1/f = 1/v + 1/u | Lens Formula: 1/f = 1/v - 1/u
Magnification: m = h'/h = -v/u (mirror), m = h'/h = v/u (lens)
Power: P = 1/f (f in m), unit dioptre D | f & R: f = R/2
Snell's Law: n₁ sin i = n₂ sin r | Refractive Index: n = c/v = real_depth/apparent_depth
Sign Convention: u always -ve; v -ve (virtual), +ve (real); f -ve (concave), +ve (convex)
Critical Angle: sin C = n_rarer / n_denser | Lens Combo: P_total = P₁ + P₂
Key Terms: Principal focus F, focal length f, pole P, centre of curvature C, optical centre O, aperture

How CBSETUTOR.ai Helps Master Light Formulas Round-the-Clock

Memorising formulas is one thing; applying them correctly under exam conditions is another. Many students struggle with sign conventions and unit conversions even after revising notes. CBSETUTOR.ai offers an AI-powered tutor available 24×7 that students can quiz on any formula from Chapter 9 Light — Reflection and Refraction. Upload a photo of a tricky mirror or lens numerical from your textbook or previous year paper, and the AI walks you through the solution step-by-step, highlighting sign logic and common pitfalls. At a flat ₹999 per month for Classes 6-12 with a 3-day free trial, it is an affordable alternative to expensive city coaching centres in Delhi, Mumbai, Bengaluru, or Hyderabad. Parents report that the instant formula clarification feature reduces last-minute panic and builds confidence before board exams.

Upload photo of any Class 10 Science numerical; AI solves it with full sign convention steps
Ask the AI tutor to quiz you on random mirror or lens formula problems for practice
Clarify doubts on magnification sign, power units, or Snell's law application anytime, even at 11 PM before exam
Flat ₹999/month covers all subjects for Classes 6-12; 3-day free trial lets you test formula help risk-free

Frequently asked questions

What is the difference between the mirror formula and the lens formula?+

The mirror formula is 1/f = 1/v + 1/u (plus sign), while the lens formula is 1/f = 1/v - 1/u (minus sign). Both relate focal length f, object distance u, and image distance v, but the sign between terms differs. Always apply New Cartesian sign convention for both.

Why is object distance u always negative in sign convention?+

Under the New Cartesian sign convention, distances are measured from the pole (mirror) or optical centre (lens). Objects are placed on the left, opposite to the direction of incident light, so u is negative by convention. This ensures consistency across all mirror and lens problems.

How do I remember which focal length is positive and which is negative?+

Concave mirrors and concave lenses have negative focal lengths because their foci lie on the object side (left). Convex mirrors and convex lenses have positive focal lengths because their foci lie on the opposite side (right). Mnemonic: 'Concave = negative, Convex = positive'.

What does negative magnification indicate?+

Negative magnification (m < 0) means the image is inverted relative to the object. Positive magnification (m > 0) means the image is erect. The magnitude |m| tells size: |m| > 1 is enlarged, |m| < 1 is diminished, |m| = 1 is same size.

How do I calculate the power of a lens and what is its unit?+

Power P = 1/f where focal length f must be in metres. The unit of power is dioptre (D), equivalent to m⁻¹. Convex lenses have positive power; concave lenses have negative power. For example, f = 25 cm = 0.25 m gives P = 1/0.25 = +4 D for a convex lens.

What is Snell's law and when do I use it?+

Snell's law states n₁ sin i = n₂ sin r, where n₁, n₂ are refractive indices of two media, i is the angle of incidence, and r is the angle of refraction. Use it whenever light crosses the boundary between two transparent media, such as air-to-glass or water-to-air, to find the angle of refraction.

How is refractive index related to the speed of light?+

Absolute refractive index n = c/v, where c is the speed of light in vacuum (3 × 10⁸ m/s) and v is the speed of light in the medium. Higher refractive index means light travels slower in that medium and bends more when entering from a less dense medium.

What is the formula for apparent depth and real depth?+

Refractive index n = (real depth) / (apparent depth). This explains why a swimming pool appears shallower than it actually is. For example, if a pool is 2 m deep and water has n = 1.33, apparent depth = 2/1.33 ≈ 1.5 m.

How do I avoid unit mistakes when calculating power?+

Always convert focal length to metres before using P = 1/f. If f is given in cm, divide by 100. For instance, f = 50 cm = 0.5 m, so P = 1/0.5 = 2 D. Writing P in cm⁻¹ instead of D will lose marks in CBSE exams.

Which formula sheet topics carry the most marks in CBSE Class 10 Science board exams?+

Mirror formula and lens formula numericals (2-3 marks each) are almost guaranteed. Magnification problems, power of lens, and Snell's law applications each appear regularly. Ray diagrams combined with formula verification can carry up to 5 marks. Definitions of principal focus and laws of reflection/refraction are common 1-2 mark theory questions.

Related resources

Important Questions: CBSE Class 10 Science Chapter 9 Light — Reflection and Refraction CBSE Class 10 Science Chapter 9 Light — Reflection and Refraction Worksheet with Answers Important Questions: CBSE Class 10 Science Chapter 8 Heredity CBSE Class 10 Science Chapter 8 Heredity Worksheet with Answers AI Tutor for Class 10: The Smart Alternative to Tuition AI Tutor for Class 10 Maths: Learn Faster with Instant Help Online Class 9 Science Tutor in Mumbai – 24/7 CBSE-Aligned AI Coaching Class 9 Mathematics Chapter 2 Polynomials — Formulas & Key Points

Keep learning — related guides

Class 10Science

Class 10 Science Chapter 11 Electricity — Formulas & Key Points

Class 10Science

CBSE Class 10 Science Chapter 11 Electricity Worksheet with Answers

Class 10Science

Class 10 Science Chapter 13 Our Environment — Formulas & Key Points

Class 10Science

Class 10 Science Chapter 12 Magnetic Effects of Electric Current — Formulas & Key Points

Class 10Science

CBSE Class 10 Science Chapter 13 Our Environment Worksheet with Answers

Class 10Science

Important Questions: CBSE Class 10 Science Chapter 13 Our Environment

Ready to give your Class 10 child the tutor that never sleeps?

CBSETUTOR.ai covers every chapter in the Class 10 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.

Start your child's 3-day free trial →